Yesterday’s news from Manchester was monstrous – two police officers, Nicola Hughes and Fiona Bone, were apparently lured to a house by a false 999 call, and then brutally murdered in a gun and grenade attack.

Any decent person would be horrified at this crime. These were two officers who worked to protect people, were not carrying any weapons with which to shoot back and were, it seems, killed in cold blood.

Inevitably, a debate has started about whether it could have been prevented. Just as inevitably, there are now calls for all police officers to be armed as a matter of course. This has been a perennial topic for debate throughout the history of the British police, which remains one of the few forces in the world whose officers do not routinely carry guns.

It’s understandable why such proposals are being put forward. Civilised people will always feel revulsion at the idea of people being shot without the ability to shoot back. However, giving the police guns would be a terrible mistake.

For a start, we should consider the Manchester case that reignited the debate. The full facts are not yet known – indeed we may well not know more until (or unless) more is reported at a trial or an inquest. There is no guarantee whatsoever, though, that had PCs Hughes and Bone been carrying guns the outcome would have been any different. In the United States, where law enforcement officers carry guns every day, there have been 33 fatalities this year already.

What we do know is that the alleged killer, Dale Cregan, was out on bail at the time, having been questioned on suspicion of involvement in at least one previous murder. It seems the system lost track of him and he disappeared, only to resurface in this horrific way.

There is always an emotional challenge in cases like this. The heartbreaking detail and personal photographs that are spread across the newspapers make us want to do something to prevent it happening again. The photos we don’t see, though, are those of the people who would die accidentally if the police were armed. We should force ourselves to remember them – those who are alive today precisely because the police don’t have guns – when making any decision.

This is not a flight of fancy, or a supposition based on guesswork. Where police forces arm all their officers, innocent people get shot.

Take, for example, the Empire State Building shooting last month. A gunman murdered a former colleague in the street, and when police in turn shot him they also wounded nine passers-by who were caught in the crossfire.

Or consider the case of Renaldo Cuevas, a shop worker who was accidentally shot by a police officer two weeks ago while trying to escape from a robbery at the bodega in the Bronx where he worked.

These cases weren’t down to malice, and I’m not spinning any conspiracy theories – but through pure accident, confusion or other factors, innocent civilians were wounded or killed.

The killings of Nicola Hughes and Fiona Bone were a disgusting crime, and we should look at how they could have been avoided (by asking how Cregan was able to go on the run while on bail over an extremely serious crime, perhaps) – but if we rush into arming the police, other innocents will die as a result. That would not be a fitting memorial.